Stability of creeping soil and implications for hillslope evolution

The geomorphic behavior of a soil-mantled hillslope undergoing diffusive creep involves a coupling between changes in land surface elevation, soil transport rates, soil production, and soil thickness. A linear stability analysis suggests that the coupled response of the soil mantle to small perturbations in soil thickness or surface topography is influenced by two factors. The diffusive-like behavior of soil creep has a stabilizing effect wherein perturbations in land surface elevation are damped. The relation between the soil production rate and soil thickness may be either stabilizing or destabilizing. A monotonically decreasing production rate with soil thickness reinforces the stabilizing effect of diffusive land surface smoothing. An increasing production rate with soil thickness has a destabilizing effect wherein perturbations in soil thickness or the soilbedrock interface are amplified, despite the presence of diffusive land surface smoothing. This coupled behavior is insensitive to the transport relation, whether the soil flux is proportional to the land surface gradient or to the product of the soil thickness and land surface gradient. The latter type of relation, nonetheless, could lead to a more complex hillslope form than might otherwise be expected for purely diffusive transport. Moreover, the response to periodic (sinusoidal) variations in the rate of stream downcutting at the lower hillslope boundary involves upslope propagation of coupled (damped) waveforms in the land surface and the soil-bedrock interface. The distance of upslope propagation goes with the square root of the product of the transport diffusion-like coefficient and the period of the downcutting rate. The upper part of the hillslope is therefore insensitive to relatively high-frequency variations in stream downcutting, so together with a stable behavior of the coupled soil-mantle-bedrock system, this part of the hillslope may exhibit a tendency toward uniform lowering, while the lower part behaves transiently. Conversely, in the presence of low-frequency variations in stream downcutting, hillslope morphology and soil thickness variations are more likely to reflect unsteady conditions over the entirety of the hillslope.